Samuele Maschio ; Alexandre Miquel - Implicative models of set theory

entics:12426 - Electronic Notes in Theoretical Informatics and Computer Science, November 23, 2023, Volume 3 - Proceedings of MFPS XXXIX - https://doi.org/10.46298/entics.12426
Implicative models of set theoryArticle

Authors: Samuele Maschio ; Alexandre Miquel

    In this paper we show that using implicative algebras one can produce models of set theory generalizing Heyting/Boolean-valued models and realizability models of (I)ZF, both in intuitionistic and classical logic. This has as consequence that any topos which is obtained from a Set-based tripos as the result of the tripos-to-topos construction hosts a model of intuitionistic or classical set theory, provided a large enough strongly inaccessible cardinal exists.


    Volume: Volume 3 - Proceedings of MFPS XXXIX
    Published on: November 23, 2023
    Accepted on: October 17, 2023
    Submitted on: October 17, 2023
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic,03B40, 03C62

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